Answer:
m<DAE = 80°
Step-by-step explanation:
Given that m<CAB = 110°,
m<DAE = (x + 4)°,
m<EAF = 30°,
m<EAF + m<DAE = m<DAF (angle addition postulate)
30° + (x + 4)° = m<DAF (substitution)
(34 + x)° = m<DAF
<DAF and <CAB are vertically opposite angles. Vertically opposite angles are said to be congruent. Therefore:
m<DAF = m<CAB
(34 + x)° = 110° (substitution)
The equation above can be used to solve for x as follows:
34 + x = 110
x = 110 - 34 (Subtracting 34 from both sides)
x = 76
m<DAE = (x + 4)°
Plug in 76, to replace x
m<DAE = 76 + 4
m<DAE = 80°
